Mass spectra of Tetraquark States from the Spinless Salpeter Equation

Abstract

The mass spectrum of tetraquark states is examined using the spinless Salpeter equation alongside the Cornell potential. Analytical wave functions are derived through a variational approach, resulting in a specific mass formula for the bound states. This study investigates the mass spectra of heavy tetraquark states within a constituent diquark-antidiquark model. We employ a spinless Salpeter equation framework, incorporating the Cornell potential to describe the interaction between the diquark and antidiquark constituents. To account for relativistic effects, we utilize first-order perturbation theory to include the leading-order kinetic energy corrections arising from the expansion of the relativistic kinetic energy operator. A variational approach is adopted to determine the ground state masses, where the optimal variational parameter ${\beta}$ is found by minimizing the system's energy and then for higher states. We systematically calculate the masses of several experimentally observed and predicted tetraquark candidates, across a range of strong coupling constant values. Our results demonstrate a sensitivity of the calculated tetraquark masses to, and the model provides theoretical mass predictions that are in reasonable agreement with experimental observations for these exotic hadronic states. This work contributes to a deeper understanding of the internal structure and dynamics of heavy tetraquarks.